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A Multi-Constrained Knapsack Approach for Educational Resource Allocation: Genetic Algorithm with Category- Specific Optimization
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DOI：10.3390/electronics14193898.png)
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Abstract
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Educational institutions face complex challenges when allocating limited teaching resources to specialized seminars, where budget, capacity, and balanced disciplinary representation must all be satisfied simultaneously. We address this for the first time in the educational domain by formulating the teacher seminar selection problem as a multi-dimensional knapsack variant with category-specific benefit multipliers. To solve it, we design a constraint-aware genetic algorithm that incorporates smart initialization, category-sensitive operators, adaptive penalties, and targeted repair mechanisms. In experiments on a realistic dataset representing multiple academic categories, our method achieved an 11.5% improvement in solution quality compared to the best constraint-aware greedy baseline while maintaining perfect constraint satisfaction (100% feasibility) vs. 0–30% for baseline methods. Statistical tests confirmed significant and practically meaningful advantages. For comprehensive benchmarking, we also implemented binary particle swarm optimization (PSO) and Tabu Search (TS) solvers with standard parameterizations. While PSO consistently produced feasible solutions with high budget utilization, its optimization quality was substantially lower than that of the GA. Notably, Tabu Search achieved the highest performance, with a mean fitness of 1557.3 compared to GA’s 1533.2, demonstrating that memory-based local search can be highly competitive for this problem structure. These findings show that metaheuristic approaches, particularly those integrating constraint-awareness into evolutionary or memory-based search, provide effective, scalable decision-support frameworks for complex, multi-constraint educational resource allocation.
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